Pairing in nuclear systems: from neutron stars to finite nuclei

We discuss several pairing-related phenomena in nuclear systems, ranging from superfluidity in neutron stars to the gradual breaking of pairs in finite nuclei. We focus on the links between many-body pairing as it evolves from the underlying nucleon-nucleon interaction and the eventual experimental and theoretical manifestations of superfluidity in infinite nuclear matter and of pairing in finite nuclei. We analyse the nature of pair correlations in nuclei and their potential impact on nuclear structure experiments. We also describe recent experimental evidence that points to a relation between pairing and phase transitions (or transformations) in finite nuclear systems. Finally, we discuss recent investigations of ground-state properties of random two-body interactions where pairing plays little role although the interactions yield interesting nuclear properties such as 0+ ground states in even-even nuclei.Comment: 74 pages, 33 figs, uses revtex4. Submitted to Reviews of Modern Physic